2024/05/02 by Chiara Castello, Castello, Chiara, Olga Polverino +3
Computer Science · Engineering · #Coding theory and cryptography #Combinatorics (math.CO) #Cooperative Communication and Network Coding #FOS: Computer and information sciences #FOS: Mathematics #Information Theory (cs.IT) #graph theory and CDMA systems
paper · pdf · doi:10.48550/arxiv.2405.01652
openalex publication_date 2024/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Subspace codes have recently been used for error correction in random network coding. In this work, we focus on one-orbit cyclic subspace codes. If S is an \mathbbFq-subspace of \mathbbFqn, then the one-orbit cyclic subspace code defined by S is Orb(S)=\αS \colon α∈ \mathbbFqn^*\,where αS=\lbrace αs \colon s∈ S\rbrace for any α∈ \mathbbFqn^*. Few classification results of subspace codes are known, therefore it is quite natural to initiate a classification of cyclic subspace codes, especially in the light of the recent classification of the isometries for cyclic subspace codes. We consider three-dimensional one-orbit cyclic subspace codes, which are divided into three families: the first one containing only Orb(\mathbbFq3); the second one containing the optimum-distance codes; and the third one whose elements are codes with minimum distance 2. We study inequivalent codes in the latter two families.